A probabilistic method for certification of analytically redundant systems

Bin Hu; Peter Seiler

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 1, page 103-116
  • ISSN: 1641-876X

Abstract

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Analytical fault detection algorithms have the potential to reduce the size, power and weight of safety-critical aerospace systems. Analytical redundancy has been successfully applied in many non-safety critical applications. However, acceptance for aerospace applications will require new methods to rigorously certify the impact of such algorithms on the overall system reliability. This paper presents a theoretical method to assess the probabilistic performance for an analytically redundant system. Specifically, a fault tolerant actuation system is considered. The system consists of dual-redundant actuators and an analytical fault detection algorithm to switch between the hardware components. The exact system failure rate per hour is computed using the law of total probability. This analysis requires knowledge of the failure rates for the hardware components. In addition, knowledge of specific probabilistic performance metrics for the fault detection logic is needed. Numerical examples are provided to demonstrate the proposed analysis method.

How to cite

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Bin Hu, and Peter Seiler. "A probabilistic method for certification of analytically redundant systems." International Journal of Applied Mathematics and Computer Science 25.1 (2015): 103-116. <http://eudml.org/doc/270194>.

@article{BinHu2015,
abstract = {Analytical fault detection algorithms have the potential to reduce the size, power and weight of safety-critical aerospace systems. Analytical redundancy has been successfully applied in many non-safety critical applications. However, acceptance for aerospace applications will require new methods to rigorously certify the impact of such algorithms on the overall system reliability. This paper presents a theoretical method to assess the probabilistic performance for an analytically redundant system. Specifically, a fault tolerant actuation system is considered. The system consists of dual-redundant actuators and an analytical fault detection algorithm to switch between the hardware components. The exact system failure rate per hour is computed using the law of total probability. This analysis requires knowledge of the failure rates for the hardware components. In addition, knowledge of specific probabilistic performance metrics for the fault detection logic is needed. Numerical examples are provided to demonstrate the proposed analysis method.},
author = {Bin Hu, Peter Seiler},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {avionics; certification; safety-critical systems; reliability; fault detection; fault-tolerant systems},
language = {eng},
number = {1},
pages = {103-116},
title = {A probabilistic method for certification of analytically redundant systems},
url = {http://eudml.org/doc/270194},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Bin Hu
AU - Peter Seiler
TI - A probabilistic method for certification of analytically redundant systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 1
SP - 103
EP - 116
AB - Analytical fault detection algorithms have the potential to reduce the size, power and weight of safety-critical aerospace systems. Analytical redundancy has been successfully applied in many non-safety critical applications. However, acceptance for aerospace applications will require new methods to rigorously certify the impact of such algorithms on the overall system reliability. This paper presents a theoretical method to assess the probabilistic performance for an analytically redundant system. Specifically, a fault tolerant actuation system is considered. The system consists of dual-redundant actuators and an analytical fault detection algorithm to switch between the hardware components. The exact system failure rate per hour is computed using the law of total probability. This analysis requires knowledge of the failure rates for the hardware components. In addition, knowledge of specific probabilistic performance metrics for the fault detection logic is needed. Numerical examples are provided to demonstrate the proposed analysis method.
LA - eng
KW - avionics; certification; safety-critical systems; reliability; fault detection; fault-tolerant systems
UR - http://eudml.org/doc/270194
ER -

References

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  1. ADDSAFE (2012). ADDSAFE: Advanced Fault Diagnosis for Sustainable Flight Guidance and Control, European 7th Framework Program, http://addsafe.deimos-space.com/. 
  2. Aldous, D. (1989). Probability Approximations via the Poisson Clumping Heuristic, Springer-Verlag, New York, NY. Zbl0679.60013
  3. Asmussen, S.R. and Glynn, P.W. (2007). Stochastic Simulation: Algorithms and Analysis, Springer, New York, NY. Zbl1126.65001
  4. Belcastro, C. and Belcastro, C. (2003). On the validation of safety critical aircraft systems, Part I: An overview of analytical and simulation method, Proceedings of the AIAA Conference of Guidance, Navigation and Control, GNC 2003, Austin, TX, USA, paper no. AIAA 2003-5559. 
  5. Bleeg, R. (1988). Commercial jet transport fly-by-wire architecture considerations, AIAA/IEEE Digital Avionics Systems Conference, San Jose, CA, USA, pp. 399-406. 
  6. Brook, D. and Evans, D.A. (1972). An approach to the probability distribution of CUSUM run length, Biometrika 59(3): 539-549. Zbl0265.62038
  7. Chen, J. and Patton, R. (1999). Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer, Boston, MA. Zbl0920.93001
  8. Collinson, R. (2011). Introduction to Avionic Systems, 3rd Edition, Springer, New York, NY. 
  9. Ding, S. (2008). Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, Springer-Verlag, Berlin. 
  10. Efimov, D., Cieslak, J., Zolghadri, A. and Henry, D. (2013). Actuator fault detection in aircraft systems: Oscillatory failure case study, Annual Reviews in Control 37(1): 180-190. 
  11. Egan, J. (1975). Signal Detection Theory and ROC Analysis, Academic Press, New York, NY. 
  12. Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer, New York, NY. Zbl0873.62116
  13. Fawcett, T. (2006). An introduction to ROC analysis, Pattern Recognition Letters 27(8): 861-874. 
  14. Freeman, P., Pandita, R., Srivastava, N. and Balas, G. (2013). Model-based and data-driven fault detection performance for a small UAV, IEEE Transactions on Mechatronics 18(4): 1300-1309. 
  15. Goupil, P. (2010). Oscillatory failure case detection in the A380 electrical flight control system by analytical redundancy, Control Engineering Practice 18(9): 1110-1119. 
  16. Goupil, P. (2011). AIRBUS state of the art and practices on FDI and FTC in flight control system, Control Engineering Practice 19(6): 524-539. 
  17. Gustafsson, F., Åslund, J., Frisk, E., Krysander, M. and Nielsen, L. (2008). On threshold optimization in fault-tolerant systems, Proceedings of the IFAC World Congress, Seoul, Korea, pp. 7883-7888. 
  18. Heller, M., Niewoehner, R. and Lawson, P.K. (2001). F/A-18E/F super hornet high-angle-of-attack control law development and testing, Journal of Aircraft 38(5): 841-847. 
  19. Hu, B. and Seiler, P. (2013). A probabilistic method for certification of analytically redundant systems, Proceedings of the 2nd International Conference of Control and Fault-Tolerant Systems, SysTol 2013, Nice, France, pp. 13-18. 
  20. Isermann, R. (2006). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer-Verlag, Berlin. 
  21. Isermann, R. and Ballé, P. (1997). Trends in the application of model-based fault detection and diagnosis of technical processes, Control Engineering Practice 5(5): 709-719. 
  22. Krasich, M. (2000). Use of fault tree analysis for evaluation of system-reliability improvements in design phase, Proceedings of the IEEE Annual Reliability and Maintainability Symposium, RAMS 2000, Los Angeles, CA, USA, pp. 1-7. 
  23. Lee, W., Grosh, D., Tillman, A. and Lie, C. (1985). Fault tree analysis, methods, and applications: A review, IEEE Transactions on Reliability 34(3): 194-203. Zbl0563.90050
  24. Lucas, J.M. and Saccucci, M.S. (1990). Exponentially weighted moving average control schemes: Properties and enhancements, Technometrics 32(1): pp. 1-12. 
  25. Murthy, D., Xie, M. and Jiang, R. (2004). Weibull Models, John Wiley & Sons, Hoboken, NJ. Zbl1047.62095
  26. Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution, IEEE Transactions on Reliability 24(5): 300-301. 
  27. Patton, R.J. and Chen, J. (1991). Robust fault detection using eigenstructure assignment: A tutorial consideration and some new results, Proceedings of the IEEE Conference on Decision and Control, CDC 1991, Brighton, UK, pp. 2242-2247. 
  28. Åslund, J., Biteus, J., Frisk, E., Krysander, M. and Nielsen, L. (2007). Safety analysis of autonomous systems by extended fault tree analysis, International Journal of Adaptive Control and Signal Processing 21(2-3): 287-298. Zbl1114.93071
  29. Rausand, M. and Hoyland, A. (2004). System Reliability Theory: Models, Statistical Methods, and Applications, Wiley-Interscience, Hoboken, NJ. Zbl1052.93001
  30. Renfrow, J., Liebler, S. and Denham, J. (1994). F-14 flight control law design, verification, and validation using computer aided engineering tools, Proceedings of the IEEE Conference on Control Applications, CCA 1994, Glasgow, UK, pp. 359-364. 
  31. Robert, C. and Casella, G. (2004). Monte Carlo Statistical Methods, Springer, New York, NY. Zbl1096.62003
  32. Rubino, G. and Tuffin, B. (2009). Rare Event Simulation Using Monte Carlo Methods, Wiley, New York, NY. Zbl1159.65003
  33. Singpurwalla, N.D. (2006). Reliability and Risk: A Bayesian Perspective, John Wiley & Sons, Chichester. Zbl1152.62070
  34. Stein, W. and Dattero, R. (1984). A new discrete Weibull distribution, IEEE Transactions on Reliability 33(2): 196-197. Zbl0563.62079
  35. United States Congress (2012). House resolution 658: FAA modernization and reform act of 2012, Section 332: Integration of civil unmanned aircraft systems into national airspace system. 
  36. Vanek, B., Bauer, P., Gozse, I., Lukatsi, M., Reti, I. and Bokor, J. (2014). Safety critical platform for mini UAS insertion into the common airspace, Proceedings of the AIAA Guidance, Navigation and Control Conference, GNC 2014, National Harbor, MD, USA, AIAA-2014-0977. 
  37. Wheeler, T.J., Seiler, P., Packard, A.K. and Balas, G.J. (2011). Performance analysis of fault detection systems based on analytically redundant linear time-invariant dynamics, Proceedings of the American Control Conference, ACC 2011, San Francisco, CA, USA, pp. 214-219. 
  38. Willsky, A.S. and Jones, H.L. (1976). A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems, IEEE Transactions on Automatic Control 21(1): 108-112. Zbl0316.93038
  39. Yeh, Y. (1996). Triple-triple redundant 777 primary flight computer, Proceedings of the 1996 IEEE Aerospace Applications Conference, Aspen, CO, USA, pp. 293-307. 
  40. Yeh, Y. (2001). Safety critical avionics for the 777 primary flight controls system, Proceedings of the 20th Digital Avionics Systems Conference, DASC 2001, Daytona Beach, FL, USA, pp. 1.C.2.1-1.C.2.11. 

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